Related papers: Model for heterogeneous reaction-diffusion systems…
Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
We explore the quasistationary regime of the Hamiltonian Mean Field Model (HMF) showing that at least three different classes of events exist, with a different diffusive behavior and with a relative frequency which depends on the size of…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents…
The simulation of stochastic reaction-diffusion systems using fine-grained representations can become computationally prohibitive when particle numbers become large. If particle numbers are sufficiently high then it may be possible to…
We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different…
Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…
Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This stochastic SIS epidemic model can be interpreted as a…
We investigate limit models resulting from a dimensional analysis of quite general heterogeneous catalysis models with fast sorption (i.e.\ exchange of mass between the bulk phase and the catalytic surface of a reactor) and fast surface…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
The thermodynamics and the dynamics of particle systems with infinite-range coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a…